a. Use the results of Example 7.5 to obtain a 95% lowerconfidence bound for the

Chapter 7, Problem 62

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QUESTION:

a. Use the results of Example 7.5 to obtain a 95% lower confidence bound for the parameter \(\lambda\) of an exponential distribution, and calculate the bound based on the data given in the example.

b. If lifetime X has an exponential distribution, the probability that lifetime exceeds t is \(P(X > t) = e^{- \lambda t}\). Use the result of part (a) to obtain a 95% lower confidence bound for the probability that breakdown time exceeds 100 min.

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QUESTION:

a. Use the results of Example 7.5 to obtain a 95% lower confidence bound for the parameter \(\lambda\) of an exponential distribution, and calculate the bound based on the data given in the example.

b. If lifetime X has an exponential distribution, the probability that lifetime exceeds t is \(P(X > t) = e^{- \lambda t}\). Use the result of part (a) to obtain a 95% lower confidence bound for the probability that breakdown time exceeds 100 min.

ANSWER:

Step 1 of 3

Given that,

In example 7.5    is chi-square distribution with   degrees of freedom. And the confidence coefficient is 95%.

 

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